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riadik2000 [5.3K]

3 years ago

6

Several students were asked what kind of animals they saw in the past week at the park. determine the ratio that compares the nu

mber of animals seen
8 dogs

2 cats

4 fish

and two lizards

2 answers:

marshall27 [118]3 years ago

4 0

Answer:

the number of animals seen to what

Step-by-step explanation:

Artist 52 [7]3 years ago

4 0

Answer:

its c

Step-by-step explanation:

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How to find the derivative of cos^2x? i seem to be confused.

slamgirl [31]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2927231

————————

You can actually use either the product rule or the chain rule for this one. Observe:

• Method I:

y = cos² x

y = cos x · cos x

Differentiate it by applying the product rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}$

The derivative of cos x is – sin x. So you have

$\mathsf{\dfrac{dy}{dx}=(-sin\,x)\cdot cos\,x+cos\,x\cdot (-sin\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=-sin\,x\cdot cos\,x-cos\,x\cdot sin\,x}$

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

—————

• Method II:

You can also treat y as a composite function:

$\left\{\!
\begin{array}{l}
\mathsf{y=u^2}\\\\
\mathsf{u=cos\,x}
\end{array}
\right.$

and then, differentiate y by applying the chain rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(u^2)\cdot \dfrac{d}{dx}(cos\,x)}$

For that first derivative with respect to u, just use the power rule, then you have

$\mathsf{\dfrac{dy}{dx}=2u^{2-1}\cdot \dfrac{d}{dx}(cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2u\cdot (-sin\,x)\qquad\quad (but~~u=cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2\,cos\,x\cdot (-sin\,x)}$

and then you get the same answer:

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>

3 0

4 years ago

What is 20,164 ÷ 71<br><br><br> Answer Soon As Posible Please

Shkiper50 [21]

The answer of this question is 284

5 0

4 years ago

Read 2 more answers

BRAINLIEST IS YOU ANSWER FAST!

horrorfan [7]

Answer:

30 is the answer!

Step-by-step explanation:

Hope you a great day!

8 0

2 years ago

Read 2 more answers

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE

Viktor [21]

Answer:

<h2> (2, -1)</h2>

Step-by-step explanation:

Given the function f(x) = 8x³ − 12x² − 48x, <em>the critical point of the function occurs at its turning point i,e at f'(x) = 0</em>

First we have to differentiate the function as shown;

$f'(x)= 3(8)x^{3-1}- 2(12)x^{2-1} - 48x^{1-1}\\ \\f'(x) = 24x^2 - 24x-48x^0\\\\f'(x) = 24x^2 - 24x-48\\\\At \ the\turning\ point\ f'(x)= 0\\24x^2 - 24x-48 = 0\\\\\\$

$Dividing \ through \ by \ 24\\\\x^2-x-2 = 0\\\\On \ factorizing\\\\x^2-2x+x-2 = 0\\\\x(x-2)+1(x-2) = 0\\\\(x-2)(x+1) = 0\\\\x-2 = 0 \ and \ x+1 = 0\\\\x = 2 \ and \ -1$

Hence the critical numbers of the function are (2, -1)

8 0

3 years ago

A rectangular field has an area of 162 m² the width of this field is 9m what is the perimeter of this field

Andru [333]

Answer:

54 m

Step-by-step explanation:

Alrighty, what have we here: an area of 162 m² and a width of 9m.

So: A=162m², W=9m, let's draw this: (see the screenshot attached)

Using the formula for area (Area = width x length) we see that:

$162m^{2} =9m*L$

Thus: (equating to L by dividing both sides by 9m)

⇒ $\frac{162m^{2} }{9m}=18m=L$

Now we have all of our dimensions, we can use the formula for the perimeter to calculate it:

$perimeter=2W+2L=2*9m+2*18m=18m+36m=54m$

And there we have our answer.

3 0

3 years ago